Question: Jack planted a mysterious bean just outside his kitchen window. It immediately sprouted 2.56 cm above the ground. Jack kept a careful log of the

Jack planted a mysterious bean just outside his kitchen window. It immediately sprouted 2.56 cm above the ground. Jack kept a careful log of the plant's growth. He measured the height of the plant each day at 8:00 A.M. and recorded these data.

a. Define variables and write an exponential equation for this pattern. If the pattern were to continue, what would be the heights on the fifth and sixth days?
b. Jack's younger brother measured the plant at 8:00 P.M. on the evening of the third day and found it to be about 63.25 cm tall. Show how to find this value mathematically. (You may need to experiment with your calculator.)
c. Find the height of the sprout at 12:00 noon on the sixth day.
d. Find the doubling time for this plant.
e. Experiment with the equation to find the day and time (to the nearest hour) when the plant reaches a height of 1 km?

Day Height (cm) 2.56 6.4 16 40100

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